Force detectors rely on resonators to transduce forces into a readable signal. Usually, these resonators operate in the linear regime and their signal appears amidst a competing background comprising thermal or quantum fluctuations as well as readout noise. Here, we demonstrate a parametric symmetry breaking transduction method that leads to a robust nonlinear force detection in the presence of noise. The force signal is encoded in the frequency at which the system jumps between two phase states which are inherently protected against phase noise. Consequently, the transduction effectively decouples from readout noise channels. For a controlled demonstration of the method, we experiment with a macroscopic doubly clamped string. Our method provides a promising paradigm for high-precision force detection.

1.
M. I.
Skolnik
,
Introduction to Radar Systems
(
McGraw Hill Book Co
.,
2000
).
2.
I. I.
Rabi
,
J. R.
Zacharias
,
S.
Millman
, and
P.
Kusch
,
Phys. Rev.
53
,
318
(
1938
).
3.
L.
Novotny
and
N.
van Hulst
,
Nat. Photonics
5
,
83
(
2011
).
5.
B. P.
Abbott
,
R.
Abbott
,
T. D.
Abbott
,
M. R.
Abernathy
,
F.
Acernese
,
K.
Ackley
,
C.
Adams
,
T.
Adams
,
P.
Addesso
,
R. X.
Adhikari
 et al (LIGO Scientific Collaboration and Virgo Collaboration. ),
Phys. Rev. Lett.
116
,
061102
(
2016
).
6.
G.
Binnig
,
C. F.
Quate
, and
C.
Gerber
,
Phys. Rev. Lett.
56
,
930
(
1986
).
7.
D.
Rugar
,
H. J.
Mamin
,
P.
Guethner
,
S. E.
Lambert
,
J. E.
Stern
,
I.
McFadyen
, and
T.
Yogi
,
J. Appl. Phys.
68
,
1169
(
1990
).
8.
H. J.
Mamin
and
D.
Rugar
,
Appl. Phys. Lett.
79
,
3358
(
2001
).
9.
J. L.
Arlett
,
J. R.
Maloney
,
B.
Gudlewski
,
M.
Muluneh
, and
M. L.
Roukes
,
Nano Lett.
6
,
1000
(
2006
).
10.
J. A.
Sidles
,
Appl. Phys. Lett.
58
,
2854
(
1991
).
11.
D.
Rugar
,
R.
Budakian
,
H. J.
Mamin
, and
B. W.
Chui
,
Nature
430
,
329
(
2004
).
12.
M.
Poggio
and
C. L.
Degen
,
Nanotechnology
21
,
342001
(
2010
).
13.
J.
Moser
,
J.
Güttinger
,
A.
Eichler
,
M. J.
Esplandiu
,
D. E.
Liu
,
M. I.
Dykman
, and
A.
Bachtold
,
Nat. Nanotechnol.
8
,
493
(
2013
).
14.
Y.
Tsaturyan
,
A.
Barg
,
E. S.
Polzik
, and
A.
Schliesser
,
Nat. Nanotechnol.
12
,
776
(
2017
).
15.
M.
Héritier
,
A.
Eichler
,
Y.
Pan
,
U.
Grob
,
I.
Shorubalko
,
M. D.
Krass
,
Y.
Tao
, and
C. L.
Degen
,
Nano Lett.
18
(
3
),
1814
1818
(
2018
).
16.
H.
Heffner
and
G.
Wade
,
J. Appl. Phys.
29
,
1321
(
1958
).
17.
P.
Penfield
and
R. P.
Rafuse
,
Varactor Applications
(
MIT Press
,
Cambridge, MA
,
1962
).
18.
L.
Kuzmin
,
K.
Likharev
,
V.
Migulin
, and
A.
Zorin
,
IEEE Trans. Magn.
19
,
618
(
1983
).
19.
B.
Yurke
,
L. R.
Corruccini
,
P. G.
Kaminsky
,
L. W.
Rupp
,
A. D.
Smith
,
A. H.
Silver
,
R. W.
Simon
, and
E. A.
Whittaker
,
Phys. Rev. A
39
,
2519
(
1989
).
20.
A.
Roy
and
M.
Devoret
, “
Quantum microwaves/micro-ondes quantiques
,”
C. R. Phys.
17
,
740
(
2016
).
21.
D.
Rugar
and
P.
Grütter
,
Phys. Rev. Lett.
67
,
699
(
1991
).
22.
A.
Szorkovszky
,
A. C.
Doherty
,
G. I.
Harris
, and
W. P.
Bowen
,
Phys. Rev. Lett.
107
,
213603
(
2011
).
23.
M.
Poot
,
K. Y.
Fong
, and
H. X.
Tang
,
Phys. Rev. A
90
,
063809
(
2014
).
24.
I.
Mahboob
,
H.
Okamoto
,
K.
Onomitsu
, and
H.
Yamaguchi
,
Phys. Rev. Lett.
113
,
167203
(
2014
).
25.
C. M.
Caves
,
Phys. Rev. D
23
,
1693
(
1981
).
26.
M. C.
Lifshitz
and
R.
Cross
, “
Nonlinear dynamics of nanomechanical and micromechanical resonators
,” in
Reviews of Nonlinear Dynamics and Complexity
(
Wiley-VCH
,
2009
), pp.
1
52
.
27.
I.
Mahboob
and
H.
Yamaguchi
,
Nat. Nanotechnol.
3
,
275
(
2008
).
28.
A.
Leuch
,
L.
Papariello
,
O.
Zilberberg
,
C. L.
Degen
,
R.
Chitra
, and
A.
Eichler
,
Phys. Rev. Lett.
117
,
214101
(
2016
).
29.
R. B.
Karabalin
,
R.
Lifshitz
,
M. C.
Cross
,
M. H.
Matheny
,
S. C.
Masmanidis
, and
M. L.
Roukes
,
Phys. Rev. Lett.
106
,
094102
(
2011
).
30.
D.
Ryvkine
and
M. I.
Dykman
,
Phys. Rev. E
74
,
061118
(
2006
).
31.
J. F.
Rhoads
and
S. W.
Shaw
,
Appl. Phys. Lett.
96
,
234101
(
2010
).
32.
L.
Papariello
,
O.
Zilberberg
,
A.
Eichler
, and
R.
Chitra
,
Phys. Rev. E
94
,
022201
(
2016
).
33.
C.
van den Broeck
and
P.
Mandel
,
Phys. Lett. A
122
,
36
(
1987
).
34.
N. G.
Stocks
,
R.
Mannella
, and
P. V. E.
McClintock
,
Phys. Rev. A
40
,
5361
(
1989
).
35.
T. R.
Albrecht
,
P.
Grütter
,
D.
Horne
, and
D.
Rugar
,
J. Appl. Phys.
69
,
668
(
1991
).

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